YES

Problem:
 f(x,x) -> a()
 f(g(x),y) -> f(x,y)

Proof:
 DP Processor:
  DPs:
   f#(g(x),y) -> f#(x,y)
  TRS:
   f(x,x) -> a()
   f(g(x),y) -> f(x,y)
  CDG Processor:
   DPs:
    f#(g(x),y) -> f#(x,y)
   TRS:
    f(x,x) -> a()
    f(g(x),y) -> f(x,y)
   graph:
    
   Qed